# American Institute of Mathematical Sciences

## Mathematical model construction of robot obstacle avoidance route optimization based on SLAM algorithm

 1 School of Mechanical and Material Engineering, Xi'an University, Xi'an 710065, China 2 Xi'an Institute of Applied Optics, Xi'an 710065, China

* Corresponding author: Jing Sun

Received  April 2019 Revised  May 2019 Published  January 2020

In order to improve the recognition accuracy and operation efficiency of obstacle avoidance routes of robots and obtain the best obstacle avoidance routes, a mathematical model of obstacle avoidance routes optimization based on SLAM algorithm is constructed. Two behavioral dynamics models of course angle dynamics and velocity dynamics are constructed. Rolling window sensor is used for route planning. Active SLAM algorithm framework is established by combining behavioral dynamics and rolling window route planning method with SLAM. The algorithm uses local sub-maps to merge rolling window map with global map, and updates the machine. On this basis, the SLAM method based on particle filter is used to construct the optimization mathematical model of the obstacle avoidance route of the robot, which can realize the effective planning of the obstacle avoidance route of the robot and obtain the optimal obstacle avoidance path. The experimental results show that the proposed model has the advantages of high recognition accuracy, good anti-interference performance and short running time. The proposed model almost coincides with the actual shortest path. The recognition accuracy is higher than 98$\%$, and the total motion time is only 460 s at 10 target points.

Citation: Jing Sun, Senlin Yang, Wei Chen, Wei Zhang, Xia Liu. Mathematical model construction of robot obstacle avoidance route optimization based on SLAM algorithm. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020253
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##### References:
Active SLAM algorithm block diagram
Map diagram of the scrolling window
Relationship between global coordinate system and rolling window coordinate system
Distribution of obstacles in the simulation map
Different model robot roadmaps for single target points
The robot of the three models moves in two target points
Robot speed change
Experimental environment map
Distribution of obstacles in simulation environment
Robot motion route by using this model
Robot motion route by using adopt geothreshold model
Robot motion route by using SAO model
Comparison of robot recognition precision of different models
Comparison of time of robot experiments in different models
Comparison of time of robot experiments in different models
Robots at 10 target points
 Target point Using this model robot Adopt geothreshold model robot Using SAO Model Robots Motion length/m Exercise time/s Motion length/m Exercise time/s Motion length/m Exercise time/s 0-1 47 49 58 62 61 65 1-2 27 35 35 52 42 58 2-3 36 42 42 66 52 71 3-4 55 57 61 72 59 70 4-5 45 47 58 53 63 55 5-6 27 36 36 51 42 49 6-7 35 41 55 66 63 65 7-8 85 62 108 75 127 70 8-9 26 33 35 55 41 56 9-10 74 58 99 88 105 90 total 457 460 587 640 655 649
 Target point Using this model robot Adopt geothreshold model robot Using SAO Model Robots Motion length/m Exercise time/s Motion length/m Exercise time/s Motion length/m Exercise time/s 0-1 47 49 58 62 61 65 1-2 27 35 35 52 42 58 2-3 36 42 42 66 52 71 3-4 55 57 61 72 59 70 4-5 45 47 58 53 63 55 5-6 27 36 36 51 42 49 6-7 35 41 55 66 63 65 7-8 85 62 108 75 127 70 8-9 26 33 35 55 41 56 9-10 74 58 99 88 105 90 total 457 460 587 640 655 649
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